An FM-CW radar measures the distance to a target, such as a vehicle traveling in front, by transmitting a continuous wave frequency-modulated in, for example, a triangular pattern. More specifically, the transmitted wave from the radar is reflected by the vehicle in front, and the reflected signal is received and mixed with a portion of the transmitted signal to produce a beat signal (radar signal). This beat signal is fast Fourier transformed to analyze the frequency. The frequency-analyzed beat signal exhibits a peak, at which the power becomes large, in correspondence with the target. The frequency corresponding to this peak is called the peak frequency. The peak frequency carries information about distance, and the peak frequency differs between the upsweep and downsweep sections of the triangular FM-CW wave because of the Doppler effect associated with the relative velocity with respect to the vehicle traveling in front. The distance and the relative velocity with respect to the vehicle traveling in front can be obtained from the peak frequencies in the upsweep and downsweep sections. If there is more than one vehicle traveling in front, a pair of peak frequencies in the upsweep and downsweep sections is generated for each vehicle. Forming such peak frequency pairs between the upsweep and downsweep sections is called pairing.
FIGS. 1A to 1C are diagrams for explaining the principle of an FM-CW radar when the relative velocity with respect to the target is 0. The transmitted wave is a triangular wave whose frequency changes as shown by a solid line in FIG. 1A. In the figure, f0 is the transmit center frequency of the transmitted wave, Δf is the FM modulation amplitude, and Tm is the repetition period. The transmitted wave is reflected from the target and received by an antenna; the received wave is shown by a dashed line in FIG. 1A. The round trip time T to and from the target is given by T=2r/C, where r is the distance (range) to the target and C is the velocity of propagation of the radio wave.
Here, the received wave is shifted in frequency from the transmitted signal (i.e., produces a beat) according to the distance between the radar and the target.
The frequency component fb of the beat signal can be expressed by the following equation.fb=fr=(4·Δf/C·Tm)r  (1)where fr is the frequency due to the range (distance).
FIGS. 2A to 2C, on the other hand, are diagrams for explaining the principle of an FM-CW radar when the relative velocity with respect to the target is v. The frequency of the transmitted wave changes as shown by a solid line in FIG. 2A. The transmitted wave is reflected from the target and received by an antenna; the received wave is shown by a dashed line in FIG. 2A. Here, the received wave is shifted in frequency from the transmitted signal (i.e., produces a beat) according to the distance between the radar and the target. In this case, as the relative velocity with respect to the target is v, a Doppler shift occurs, and the beat frequency component fb can be expressed by the following equation.fb=fr±fd=(4·Δf/C·Tm)r±(2·f0/C)v  (2)where fr is the frequency due to the range, and fd is the frequency due to the velocity.
In the above equation, the peak frequency fbup in the upsweep section and the peak frequency fbdn in the downsweep section are given byfbup=fr−fd=(4·Δf/C·Tm)r−(2·f0/C)v  (3)fbdn=fr+fd=(4·Δf/C·Tm)r+(2·f0/C)v  (4)
The symbols in the above equations have the following meanings.
fb: Transmit/receive beat frequency
fr: Range (distance) frequency
fd: Velocity frequency
f0: Center frequency of transmitted wave
Δf: Frequency modulation amplitude
Tm: Period of modulation wave
C: Velocity of light
T: Round trip time of radio wave to and from target object
r: Range (distance) to target object
v: Relative velocity with respect to target object
FIG. 3 is a diagram showing one configuration example of an FM-CW radar. As shown, a modulating signal generator 1 applies a modulating signal to a voltage-controlled oscillator 2 for frequency modulation, and the frequency-modulated wave is transmitted out from a transmitting antenna AT, while a portion of the transmitted signal is separated and fed into a frequency converter 3 such as a mixer. The signal reflected from a target, such as a vehicle traveling in front, is received by a receiving antenna AR, and the received signal is mixed with the output signal of the voltage-controlled oscillator 2 to produce a beat signal. The beat signal is passed through a baseband filter 4, and is converted by an A/D converter 5 into a digital signal; the digital signal is then supplied to a CPU 6 where signal processing, such as a fast Fourier transform, is applied to the digital signal to obtain the distance and the relative velocity.
From the above equations (3) and (4)fr=(fbdn+fbup)/2
Since fr=(4·Δf/C·Tm)r, the relative distance r is given byr=(C·Tm/8·Δf)(fbdn+fbup)  (5)
Similarly, from the above equations (3) and (4)fd=(fbdn−fbup)/2
Since fd=(2·f0/C)v, the relative velocity v is given byv=(C/4f0)(fbdn−fbup)  (6)
As can be seen from the above equations (5) and (6), the relative velocity v is proportional to the difference between fbdn and fbup, and the relative distance r is proportional to the sum of fbdn and fbup. Therefore, the values of fbdn and fbup decrease as the relative distance r decreases.
FIGS. 4A to 4C are diagrams showing the positional relationship between the upsweep and downsweep peak frequencies when there is a target approaching at a high relative velocity and the relative distance is therefore rapidly decreasing. In the figures, the relative distance is rapidly decreasing as shown in FIGS. 4A, 4B, and 4C in this order. When the target is approaching at a high relative velocity, the difference between the upsweep and downsweep peak frequencies fbup and fbdn increases. On the other hand, when the relative distance decreases, the values of fbup and fbdn decrease; therefore, the values of fbdn and fbup approach zero as shown in FIGS. 4A, 4B, and 4C in this order, and eventually, the upsweep peak frequency fbup enters the negative frequency range as shown in FIG. 4C. If this happens, the upsweep peak frequency fbup can no longer be detected, resulting in an inability to detect the target. Furthermore, when the upsweep peak frequency fbup enters the negative frequency range, a peak due to a folded frequency f′bup occurs as shown by a dashed line and, as a result, erroneous pairing is done, thus resulting in erroneous measurements of the relative distance and the relative velocity.
FIGS. 5A to 5C are diagrams showing the positional relationship between the upsweep and downsweep peak frequencies when there is a target receding at a high relative velocity and the relative distance is therefore rapidly increasing. In the figures, the relative distance is rapidly increasing as shown in FIGS. 5A, 5B, and 5C in this order. When the target is receding at a high relative velocity, the difference between the upsweep and downsweep peak frequencies fbup and fbdn increases. On the other hand, when the relative distance increases, the values of fbup and fbdn increase; therefore, the values of fbdn and fbup increase as shown in FIGS. 5A, 5B, and 5C in this order, and eventually, the upsweep peak frequency fbup exceeds the detection frequency range fx as shown in FIG. 5C. If this happens, the upsweep peak frequency fbup can no longer be detected, resulting in an inability to detect the target. Furthermore, when the upsweep peak frequency fbup exceeds the detection frequency range, a peak due to a folded frequency f′bup occurs as shown by a dashed line, and as a result, erroneous pairing is done, thus resulting in erroneous measurements of the relative distance and the relative velocity.
In a prior art signal processing apparatus for an FM-CW radar, the folded peak frequency is detected by analyzing the frequency obtained when the sampling frequency is set to one half of the normal sampling frequency, and pairing is done between the upsweep and downsweep peak frequencies after converting the folded peak frequency into a peak frequency that would be obtained if there were no frequency folding (for example, refer to Japanese Unexamined Patent Publication No. H11-271426).
Further, a pulse-repetition frequency-pulse Doppler radar is disclosed that measures a correct distance by avoiding the influence of the frequency folding (for example, refer to Japanese Examined Patent Publication No. H06-70673).